On a multicompartment age-distribution model of cell growth

Begg, Ronald; Wall, David J. N.; Wake, G. C.

doi:10.1093/imamat/hxq010

Cited by 8 publications

(5 citation statements)

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“…Phase steady-state conditions have also been considered in other mathematical models such as Begg et al (2010), where the terms balanced exponential growth, or asynchronous exponential growth, are also used to describe this situation. However, throughout this paper, we will continue to refer to this condition as phase steadystate, or unchanging environmental conditions.…”

Section: Steady-state Conditionsmentioning

confidence: 99%

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A Mathematical Model of Cell Cycle Progression Applied to the MCF-7 Breast Cancer Cell Line

2011

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In this paper, we present a model of cell cycle progression and apply it to cells of the MCF-7 breast cancer cell line. We consider cells existing in the three typical cell cycle phases determined using flow cytometry: the G1, S, and G2/M phases. We further break each phase up into model phases in order to capture certain features such as cells remaining in phases for a minimum amount of time. The model is also able to capture the environmentally responsive part of the G1 phase, allowing for quantification of the number of environmentally responsive cells at each point in time. The model parameters are carefully chosen using data from various sources in the biological literature. The model is then validated against a variety of experiments, and the excellent fit with experimental results allows for insight into the mechanisms that influence observed biological phenomena. In particular, the model is used to question the common assumption that a 'slow cycling population' is necessary to explain some results. Finally, an extension is proposed, where cell death is included in order to accurately model the effects of tamoxifen, a common first line anticancer drug in breast cancer patients. We conclude that the model has strong potential to be used as an aid in future experiments to gain further insight into cell cycle progression and cell death.

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Section: Steady-state Conditionsmentioning

confidence: 99%

“…However, such models are complex and require many parameters to define the process. Analysis of such age-structured models has been performed in Begg et al (2010), which address issues of uniqueness and stability of equations describing cell cycle progression.…”

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confidence: 99%

A Mathematical Model of Cell Cycle Progression Applied to the MCF-7 Breast Cancer Cell Line

2011

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“…The exponential rate at which oscillations decay has not been found in models similar to CCP-PBM with three distributed compartments. 32 However, numerical simulations can be run for specific cases and relevant parameters such as the amplitude of the oscillations or the time to steady state can be obtained.…”

Section: Resultsmentioning

confidence: 99%

“…It is worth mentioning that previous steady state analyses performed on one-compartment models have determined analytically the rate at which oscillations decay over time. The exponential rate at which oscillations decay has not been found in models similar to CCP-PBM with three distributed compartments . However, numerical simulations can be run for specific cases and relevant parameters such as the amplitude of the oscillations or the time to steady state can be obtained.…”

Section: Resultsmentioning

confidence: 99%

Selecting a Differential Equation Cell Cycle Model for Simulating Leukemia Treatment

Fuentes-Garí¹,

Misener²,

Georgiadis³

et al. 2015

Ind. Eng. Chem. Res.

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This manuscript studies three differential equation models of the leukemia cell cycle: a population balance model (PBM) using intracellular protein expression levels as state variables representing phase progress; a delay differential equation model (DDE) with temporal phase durations as delays; and an ordinary differential equation model (ODE) of inter-phase progression. In each type of model, global sensitivity analysis determines the most significant parameters while parameter estimation fits experimental data. In order to compare models based on the output of their structural properties, an expected behavior was defined, and each model was coupled to a pharmacokinetic/pharmacodynamic model of chemotherapy delivery. Results suggest that the particular cell cycle model chosen highly affects the simulated treatment outcome, given the same steady state kinetic parameters and drug dosage/scheduling. The manuscript shows how cell cycle models should be selected according to the complexity, sensitivity and parameter availability of the application envisioned.2

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“…The model has been applied to tumour growth [3] and the growth of plankton [4]. Recently, a multicompartment age-distribution model has been developed by Begg et al [6].…”

Section: Introductionmentioning

confidence: 99%

Eigenfunctions Arising From a First-Order Functional Differential Equation in a Cell Growth Model

Brunt

Vlieg-Hulstman

2010

ANZIAM J.

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A boundary-value problem for cell growth leads to an eigenvalue problem. In this paper some properties of the eigenfunctions are studied. The first eigenfunction is a probability density function and is of importance in the cell growth model. We sharpen an earlier uniqueness result and show that the distribution is unimodal. We then show that the higher eigenfunctions have nested zeros. We show that the eigenfunctions are not mutually orthogonal, but that there are certain orthogonality relations that effectively partition the set of eigenfunctions into two sets.2000 Mathematics subject classification: primary 34K06; secondary 34K10.

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On a multicompartment age-distribution model of cell growth

Cited by 8 publications

References 0 publications

A Mathematical Model of Cell Cycle Progression Applied to the MCF-7 Breast Cancer Cell Line

A Mathematical Model of Cell Cycle Progression Applied to the MCF-7 Breast Cancer Cell Line

Selecting a Differential Equation Cell Cycle Model for Simulating Leukemia Treatment

Eigenfunctions Arising From a First-Order Functional Differential Equation in a Cell Growth Model

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